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```Isothermal* and Adiabatics.

be actually measured (see Fig. 325); but as these curves have
definite formulae, it is easier to use algebraic methods.    Then,

y

Area of curve having formula PV = C        is PV x loge ,

vi

and as PV = cr. and  = the ratio of expansion r.

v,

Area = cr loge r.              (Seep. 1131.)
(Use hyperbolic logarithms, and see Fig. 612)
Area of curve having formula PVW = C       is ------??

71  I

Isothermals and Adiabatics.If a gas expand, and
advance a piston against a resistance, it does work requiring
expenditure of heat. Such heat being abstracted from the gas,
the temperature of the latter falls; but if heat be supplied just
as fast as it is abstracted, viz. equal to the work done, the tem-
perature will remain constant, the expansion be according to
Boyle (PV =» C), and the curve be called an isothermal.

If no heat be supplied, the pressure-volume curve will fall
below the hyperbola, as in Fig. 613, according to the formula
PV" = C, and be then termed an adiatiatic. Similarly, in com-
pressing, the adiabatic will rise above the isothermal, because
the gas becomes t heated by work done upon it (Fig. 614).
(See Appendix IL,p. 879.)

Adiabatic Exponent.The value of n will now be found

Area of curve

n _

('I-'

External work,

Total work = Internal work + External work

- <- - '->    -->_+,K-K') - h - o (SSf

* Notice change of sign in two places in order to balance.```